Syllabus:
- Basic concepts of forward and inverse problems
- Ill-posedness of inverse problems,
- condition number, non-uniqueness and stability of solutions;
- L1, L2 and Lp norms
- overdetermined, underdetermined and mixed determined inverse problems,
- quasi- linear and non-linear methods including Tikhonov’s regularization method,
- Singular Value Decomposition,
- Backus-Gilbert method,
- simulated annealing,
- genetic algorithms,
- swarm intelligence,
- machine learning and artificial neural networks.
- Statistics of misfit and likelihood,
- Bayesian construction of posterior probabilities,
- sparsity promoting L1 optimization.
- Ambiguity and uncertainty in geophysical interpretation.
- Optimization
- Null-Space